Hey Mary Ann,
These were and still are issued by the United States Army only. The other services have their own. They date back before WWII and some of them are actually sterling silver. The older ones have a safety pin type device to secure them to the uniform and the later ones have two straight push pins. I believe that the Army began using these around 1921 just after WWI. I am sitting here looking at a photo of my Dad from WWII and he is sporting his in the photo. They come in three flavors. Yours is the Expert and there is a Sharpshooter and then a Marksman. They rank in that order for shooting proficiency. The better the score, the higher the medal. The little attachments can be added for many different weapons. If a soldier qualifies as an Expert with one weapon and as a Marksman with another, the soldier gets two medals, one each for each level of qualification.
Yours appears to be the WWII vintage type and should be marked with Sterling on the back. It is in really good shape. Don't clean it to a point that you remove the black off of it. The black coloring is part of the badge. Use a jewelers cloth to clean the silver part only if you do anything.
Hope this helps,
DaChief